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Advanced in Mach-Zehnder Interferometer Using Windowed Fourier Transform to Analyse Coupled Heat and Mass Transfer

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Advances in Visualization and Optimization Techniques for Multidisciplinary Research

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

Series of thermodiffusion experiments using optical digital interferometry (ODI) have been conducted onboard the International Space Station. Conventionally, the two-dimensional (2D) fast Fourier transform (FFT) fringe analysis technique has been applied as a fast and reliable technique to extract data. In this study, for the first time, the windowed Fourier transform (WFT) method is used to analyse the same experiments. In this method, a Fourier transformation is applied on the fringes at two different stages: initially, during the filtration of the non-zero peaks and then on the wrapped phase image. We provide a detailed comparison between FFT and WFT results of binary and ternary mixtures for ODI thermodiffusion experiments. The substantial enhancements of this method are presented and discussed for different experiments conducted for both binary and ternary mixtures. We show that while disturbances in the phase fringe pattern can cause significant error in FFT techniques, if the windowed Fourier filtration (WFF) parameters are properly chosen this type of noise can be eliminated during WFF analysis. The importance of replacing the FFT method becomes more pronounced for the ternary system, as this method fails to reconcile reliable concentration profiles. The results of this chapter can show that the application of the windowed Fourier transform in optical digital interferometry investigations show improved results over the same experiments analysed using FFT methods, especially for experiments involving very small heat and mass fluxes such as the Soret effect in multicomponent mixtures.

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Abbreviations

Change in refractive index:

\( \Delta n \)

Coordinate index of pixel:

i, j

Coordinate system:

x, y

Fourier transform of coordinate:

\( u, v, \xi, \eta \)

Initial concentration:

cO

Molecular diffusion coefficient:

D (m2 s−1)

Maximum concentration difference:

\( \Delta C \)

Non zero picks, Fourier transform:

C, C*

Number of pixels in x, y direction:

m, n

Optical length of the cell:

L (mm)

Phase distribution:

\( \Delta \phi \)

Soret coefficient:

ST (K−1)

Temperature difference:

\( \Delta {\text{T}}\,({\text{K}}) \)

Time:

\( t\,(\text{s}) \)

Thermodiffusion coefficient:

DT (m2 s−1 K−1)

Vibration amplitude:

A (mm)

WFT spectrum:

\( Sf \)

Concentration contrast factor:

\( \left( {\partial n\partial c} \right)_{p.T} \left( - \right) \)

Density:

\( \rho \,\left( {{\text{kg/m}}^{3} } \right) \)

Interference phase:

\( \upphi \)

Laser wavelength:

\( \uplambda\,({\text{nm}}) \)

Mixture viscosity:

\( \uplambda\,({\text{nm}}) \)

Relaxation time:

\( \uptau\,({\text{s}}) \)

Temperature contrast factor:

\( \left( {\partial n\partial T} \right)_{p.c} \,\left( {{1/\text{K}}} \right) \)

Thermal diffusivity:

\( \upchi\,({\text{m}}^{2} /{\text{s}}) \)

Standard deviations:

\( \delta_{x},\,\delta_{y} \)

Experimental:

exp

Hour:

hr

Minute:

min

Reference:

ref

Thermal:

th

Threshold:

thr

Steady:

st

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Acknowledgements

Authors would like to acknowledge the financial support of the Canadian Space Agency (CSA) and the Natural Sciences and Engineering Research Council of Canada (NSERC) in funding this work.

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  1. 350 Victoria Street, Toronto, ON, Canada

    Amirhossein Ahadi & M. Ziad Saghir

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  1. Amirhossein Ahadi
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Correspondence to Amirhossein Ahadi .

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Editors and Affiliations

  1. Vesalius College (VeCo), Vrije Universiteit Brussel (VUB), Brussels, Belgium

    Dean Vucinic

  2. Mechanical Engineering Department, Universidade Federal Fluminense, Niterói—Rio de Janeiro, Brazil

    Fabiana Rodrigues Leta

  3. Department of Mechanical Engineering, SCMS School of Engineering and Technology, Karukutty, Ernakulam, Kerala, India

    Sheeja Janardhanan

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Ahadi, A., Saghir, M.Z. (2020). Advanced in Mach-Zehnder Interferometer Using Windowed Fourier Transform to Analyse Coupled Heat and Mass Transfer. In: Vucinic, D., Rodrigues Leta, F., Janardhanan, S. (eds) Advances in Visualization and Optimization Techniques for Multidisciplinary Research. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-9806-3_1

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  • DOI: https://doi.org/10.1007/978-981-13-9806-3_1

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